# Re: A new paradigm?(On pitch and periodicity (was "correction to post"))

```Pim,

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Sometimes it's hard to get a reaction when you are trying to replace a paradigm, as the silence here illustrates. I didn't really get into the new ideas of your book much, but I have some comments on the introductory material about why you reject the current paradigm.
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You discuss and reject two wave concepts: first, the pressure sound wave that travels so fast that wavelengths will always be long compared to the size of the cochlea, and second, "capillary" or "interfacial" waves, presumably meaning those water surface waves where gravity provides the restoring force. Of course, neither of these can be the explanation for how the cochlea works. But they are not invoked that way, normally. The traveling wave in the cochlea is sort of like water surface gravity waves, but the restoring force can't be gravity, as you note, since there are not different fluid densities. Rather, the restoring force is due to the compliance of the basilar membrane. If you go back to Airy's and Lamb's analysis of the physics of gravity waves using 2D inviscid incompressible irrotational approximations, and substitute the compliance of the BM for the surface restoring force of gravity, you can derive the wave equations that describe the (approximate) physics of waves in the cochlea, in the 2D case (which is much better than the 1D long-wave and short-wave approximations, and not quite as comprehensive as a 3D model, which is harder). Right at the BM, you also can't completely get away with the inviscid assumption, since there must be a viscous boundary layer providing a drag force where the fluid velocity is discontinuous from the zero longitudinal velocity of the BM; but that can be lumped into BM impedance.
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You also attribute to Lighthill some strange wrong ideas about transmission lines only being able to transmit energy near their resonance. Actually, he showed the opposite: that a sinusoidal wave will propagate until the point where the transmission line resonance gets low enough to match the wave frequency, and at that point it will slow down to zero velocity and die out. This is not exactly how the cochlea works (the BM is not very resonant), but not a bad concept from base to near the best place.
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You conclude that "the existence of two sound energy transport phenomena with different transfer velocities within this tiny cochlear volume of perilymph fluid as suggested by Lighthill is impossible." Yet all observations do see a slow wave, much slower than the speed of sound, and basic mathematical physics of the same sort that has been working well for over 100 years to describe waves in fluids predicts exactly that behavior. Some may quibble that it has not been conclusively proved that the observed slow wave carries energy; but no workable alternative has been put forward, and no experiment convincingly contradicts this main hypothesis of the current paradigm, as far as I know. I know some on this list will probably say I'm wrong, now that I've opened the door.
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I was intrigued by your pointing out that the thin Reissner's membrane, even though very flexible, will disrupt some aspects of the assumed physics of the fluid behavior, since the longitudinal velocity will not be continuous across it and it will introduce viscous drag to longitudinal flow. It's a good point that I hadn't thought of before, and it's not clear exactly what the effect is. Near "resonance" however, in the short-wave region, the fluid movement is all very close to the BM, well inside scala media and away from RM; so the normal 2D wave equations should work well there at least.
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It sounds like you're trying to get away from a Helmholtz-like conception of resonators or places responding to frequencies, and replace it with a more time-domain approach that works for a lot of pitch phenomena. But it will work better to put that time-domain mechnanisms AFTER the what the cochlea does. Each hair cell is a "tap" on the BM, reporting a time-domain waveform as filtered by the traveling-wave mechanism; that's where the pitch-processing nonlinear time-domain operations start...
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Dick

At 6:39 PM -0400 9/9/11, Willem Christiaan Heerens wrote:
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```Dear List,

original start of all this  was the question of Nedra Floyd-Pautler about
auditory illusions in relation to hearing aids.
But it was the comment of Randy Randhawa addressed to her with the
following content:

In my opinion the most enduring (over 200 years) of all
auditory "illusions" is what has been called the "missing fundamental". The
fact that this has not been satisfactorily resolved by the tortured use of
existing signal processing techniques leads some, including yours truly, to
believe that the auditory system has figured out a unique way to do
frequency analysis and to meet the dictum in biology that "form follows
function". Taking into account where we are and the discussions that take
place, e.g. this forum, it is interesting that there has been no discussion
as to why the cochlear has the shape it does. Therefore some experimental
phenomenon that we may call as an illusion, could have a very natural
consequence of how frequency analysis is done. One is lead to believe that
we are truly very far from understanding how the auditory system works and
therefore hearing aid designs are a bit of a hoax foisted on
the "proletariat". Sorry if I sound a bit harsh, but I think it is time
people recognized that the emperor has not clothes.

And sorry for those who have other ideas, I completely agree with Randy¹s
remarks here above. And I have reasons for this opinion.

Although not being an auditory expert, but having an academic applied
physics background I have studied already for more than ten years the
functionality of the mammalian hearing sense.
Together with ENT MD J. Alexander de Ru I have recently published a booklet
with the following title:

Applying Physics Makes Auditory Sense

With subtitle:

This booklet describes in the first chapter ­ Introduction ­ the objections
we have against a number of existing hypotheses, simply because they are at
variance with general laws of physics.

In the second chapter ­ The new hypothesis ­ we describe how based on our
findings the mammalian hearing sense can function in such a way that it is
on the one hand in full agreement with the rules and laws of general
physics and mechanics and that on the other hand it explains clearly all
the salient mysteries and anomalies, has the potential to explain even much
more yet unclear details in our auditory system and predicts other
verifiable hearing phenomena.

The third chapter ­ Methods and experiments for verification ­ deals with
perception experiments in which the ?missing fundamental¹ and the ?strike
note of bells¹ are found to be normal hearing phenomena, so no illusions,
while the ?shift in pitch¹, described in literature as result of a uniform
frequency shift in higher ?incomplete harmonic¹ sound complexes, is found
as an illusion, based on subjective perception of musically trained
experimenters.

The other four chapters describe details about the functioning of the
cochlea.

If you combine this with the formulation of Richard Lyon in his comment to
Ita Katz:

It would be much more robust to say that "The pitch is determined based on
an approximately common periodicity of outputs of the cochlea," which I
believe is consistent with your intent.

Why is this better?

First, it doesn't say the periodicity is determined; what is determined is
the pitch (even that is a bit of stretch, but let's go with it).
Second, it doesn't depend on whether the signal is periodic, that is,
whether harmonics exist.
Third, it doesn't depend on being able to isolate and separately
characterize components, harmonic or otherwise.
Fourth, it doesn't need "multiples" (or divisors), but relies on the
property of periodicity that a signal with a given period is also periodic
at multiples of that period, so it only needs to look for "common"
periodicities--which doesn't require any arithmetic, just simple neural
circuits.  Fifth, it admits approximation, so that things like "the strike
note of a chime" and noise-based pitch can be accommodated.
Sixth, it recognizes that the cochlea has a role in pitch perception.  It's
still not complete or perfect, but I think presents a better picture of how
it actually works, in a form that can be realistically modeled.

You will observe that all these six aspects are forming parts of the
concept we have named a new paradigm in hearing.

You can download the e-book version of our booklet from the website of the
University of Utrecht:

http://igitur-archive.library.uu.nl/med/2011-0204-200555/UUindex.html

this message

Regards

Pim Heerens

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